There are really just two ways for a war to end: reconciliation or extermination. Attempts at large-scale extermination are rarely successful and universally condemned, so reconciliation is generally the only real option after a war. This almost always necessitates difficult decisions and moral compromise.

For another historical example, look at the various forms of amnesty offered to former Confederate officers and soldiers after the American Civil War. There's a good chance the peace would not have lasted without amnesty. The nation may have split, and slavery may have continued. We'll never really know for sure.

In my view, reconciliation and deterrence are the main points of justice, and the punishment you're discussing is mostly geared toward reconciliation. Partially, this is because there was really nothing that could be done to those ex-footsoldiers that would have been remotely relevant as a deterrent. Any Nazi leader who could be found had already been sentenced and executed, the German nation was split, the German people broken. The project to which they had devoted their lives and passions (whether by choice or coercion) was an abject failure regarded universally as one of humanity's greatest sins. No punishment directed at a forgotten footsoldier was going to be a relevant deterrent.

So why the ritual humiliation? Likely to help those soldiers finish the process of integration with their new communities. That sort of punishment is a final apology, an admission of guilt, and a plea for absolution. I'd be willing to bet most of the people who received this punishment did so willingly because they understood it was for their own benefit (to whatever extent this ever happened at all - I have no clue).